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log_test.go
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log_test.go
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package floatutils_test
import (
"math"
"math/big"
"math/rand"
"testing"
"github.com/ALTree/floatutils"
)
func TestLog(t *testing.T) {
for _, test := range []struct {
x string
want string
}{
// 350 decimal digits are enough to give us up to 1000 binary digits
{"0.5", "-0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335011536449795523912047517268157493206515552473413952588295045300709532636664265410423915781495204374043038550080194417064167151864471283996817178454696"},
{"0.25", "-1.3862943611198906188344642429163531361510002687205105082413600189867872439393894312117266539928373750840029620411413714673710404715162611140653415032701519238614551416567428703806140772477833469422467002307289959104782409503453631498641303110494682790517659009060141906527332853082084783156299040874808607710016038883412833430372894256799363435690939"},
{"0.0125", "-4.3820266346738816122696878190588939118276018917095387383953679294477534755864366270535871860788543609679722271039983058344660861723571984277642996240040095752750899208106689864147210106979082189417635556550588715983462075888842670124944153533207460860520530946333864410280342429017041970928492563533263928706772062013203262792640026952942261381891629"},
{"1e-100", "-230.25850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220"},
{"1e-100000", "-230258.50929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220"},
{"1", "0.0"},
{"2", "0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335011536449795523912047517268157493206515552473413952588295045300709532636664265410423915781495204374043038550080194417064167151864471283996817178454696"},
{"10", "2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220"},
{"1e5", "11.512925464970228420089957273421821038005507443143864880166639504837863048386762401179986025447991491709838920211431243167047627325414033783331436845493908447414536041627773404218999474131165992641967526544826888663144230816831111438491099433732718337372021216371825775244671574696957398097022001110525508570874001844042006323540342783871608114177610"},
{"1e10", "23.025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220"},
{"1e100", "230.25850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220"},
{"1e100000", "230258.50929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220"},
} {
for _, prec := range []uint{24, 53, 64, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000} {
want := new(big.Float).SetPrec(prec)
want.Parse(test.want, 10)
x := new(big.Float).SetPrec(prec + 16) // see sqrt_test.go
x.Parse(test.x, 10)
z := floatutils.Log(x)
wantMaxPrec, _, err := big.ParseFloat(test.want, 0, maxPrec, big.ToNearestEven)
if err != nil {
t.Errorf("prec = %d, parse(%s): %v", maxPrec, test.want, err)
}
acc := big.Accuracy(want.Cmp(wantMaxPrec))
z.SetPrec(prec)
if z.Cmp(want) != 0 || z.Acc() != acc {
t.Errorf("prec = %d, Log(%v) = %g (%v); want %g (%v)", prec, test.x, z, z.Acc(), want, acc)
}
}
}
}
func TestLog32(t *testing.T) {
for i := 0; i < 1e4; i++ {
r := rand.Float32() * 1e3
x := big.NewFloat(float64(r)).SetPrec(24)
z, acc := floatutils.Log(x).Float32()
want := math.Log(float64(r))
if z != float32(want) || acc != big.Exact {
t.Errorf("Log(%f) =\n got %b (%s);\nwant %b (Exact)", x, z, acc, want)
}
}
}
func TestLog32Small(t *testing.T) {
for i := 0; i < 1e4; i++ {
r := rand.Float32() * 1e-30
x := big.NewFloat(float64(r)).SetPrec(24)
z, acc := floatutils.Log(x).Float32()
want := math.Log(float64(r))
if z != float32(want) || acc != big.Exact {
t.Errorf("Log(%f) =\n got %b (%s);\nwant %b (Exact)", x, z, acc, want)
}
}
}
func TestLog32Big(t *testing.T) {
for i := 0; i < 1e4; i++ {
r := rand.Float32() * 1e30
x := big.NewFloat(float64(r)).SetPrec(24)
z, acc := floatutils.Log(x).Float32()
want := math.Log(float64(r))
if z != float32(want) || acc != big.Exact {
t.Errorf("Log(%f) =\n got %b (%s);\nwant %b (Exact)", x, z, acc, want)
}
}
}
// Unfortunately, the Go math.Log function is not completely
// accurate, so it doesn't make sense to require 100%
// compatibility with it, since it happens that math.Log
// returns a result with the last bit off (see Issue #9546).
//
// For this reason, we just require that the result is
// within distance 1e-14 from what math.Log returns
// (1e-12 for very small values).
func TestLog64(t *testing.T) {
for i := 0; i < 1e4; i++ {
r := rand.Float64() * 1e3
x := big.NewFloat(r).SetPrec(53)
z, acc := floatutils.Log(x).Float64()
want := math.Log(r)
if math.Abs(z-want) > 1e-14 || acc != big.Exact {
t.Errorf("Log(%g) =\n got %g (%s);\nwant %g (Exact)", x, z, acc, want)
}
}
}
func TestLog64Small(t *testing.T) {
for i := 0; i < 1e4; i++ {
r := rand.Float64() * 1e-300
x := big.NewFloat(r).SetPrec(53)
z, acc := floatutils.Log(x).Float64()
want := math.Log(r)
if math.Abs(z-want) > 1e-12 || acc != big.Exact { // 1e-12 for very small values
t.Errorf("Log(%g) =\n got %g (%s);\nwant %g (Exact)", x, z, acc, want)
}
}
}
func TestLog64Big(t *testing.T) {
for i := 0; i < 1e4; i++ {
r := rand.Float64() * 1e300
x := big.NewFloat(r).SetPrec(53)
z, acc := floatutils.Log(x).Float64()
want := math.Log(r)
if math.Abs(z-want) > 1e-14 || acc != big.Exact {
t.Errorf("Log(%g) =\n got %g (%s);\nwant %g (Exact)", x, z, acc, want)
}
}
}
func TestLogSpecialValues(t *testing.T) {
for i, f := range []float64{
+0.0,
-0.0,
math.Inf(+1),
} {
x := big.NewFloat(f).SetPrec(53)
z, acc := floatutils.Log(x).Float64()
want := math.Log(f)
if z != want || acc != big.Exact {
t.Errorf("%d) Log(%f) =\n got %b (%s);\nwant %b (Exact)", i, f, z, acc, want)
}
}
}
// ---------- Benchmarks ----------
func benchmarkLog(num float64, prec uint, b *testing.B) {
b.ReportAllocs()
x := new(big.Float).SetPrec(prec).SetFloat64(num)
for n := 0; n < b.N; n++ {
floatutils.Log(x)
}
}
func BenchmarkLog2Prec53(b *testing.B) { benchmarkLog(2, 53, b) }
func BenchmarkLog2Prec64(b *testing.B) { benchmarkLog(2, 64, b) }
func BenchmarkLog2Prec100(b *testing.B) { benchmarkLog(2, 1e2, b) }
func BenchmarkLog2Prec250(b *testing.B) { benchmarkLog(2, 250, b) }
func BenchmarkLog2Prec500(b *testing.B) { benchmarkLog(2, 500, b) }
func BenchmarkLog2Prec1000(b *testing.B) { benchmarkLog(2, 1e3, b) }
func BenchmarkLog2Prec10000(b *testing.B) { benchmarkLog(2, 1e4, b) }